Abstract: The quasi-persistent neutron star X-ray transient and eclipsing binary EXO 0748−676 recently started the transition to quiescence following an accretion outburst that lasted more than 24 years. We report on two Chandra and 12 Swift observations performed within five months after the end of the outburst. The Chandra spectrum is composed of a soft, thermal component that fits to a neutron star atmosphere model with kT ∞ ∼ 0.12 keV , joined by a hard power-law tail that contributes ∼20 per cent of the total 0.5–10 keV unabsorbed flux. The combined Chandra/Swift data set reveals a relatively hot and luminous quiescent system with a temperature of kT ∞ ∼ 0.11–0.13 keV and a bolometric thermal luminosity of ∼8.1 × 10 33 –1.6 × 10 34 (d/7.4 kpc) 2 erg s −1 . We discuss our results in the context of cooling neutron star models.